thermal thermal thermal 2 (25) 5. Sno w begins falling continuously at midnight
ID: 2073701 • Letter: T
Question
thermal thermal thermal 2 (25) 5. Sno w begins falling continuously at midnight until 3:00 am at the rate of 0.6 pump snow melting system which supplies 1.5E5 BTUhr to the slab. b/ft.hr on the 34 concrete. Sensors immediately detect this and turn on the heat Assuming that the slab remains at 34 and that no other heat is lost to the soil or surroundings, will the snow be melted before the morning commuter rush at 6:00 am? What fraction of it is left? Provide justification for your answers. Is snow melted: Units: yes/no Units: percent Fraction of remaining snow:Explanation / Answer
explanation for part c:
so you're given a rate function g(t) [cubic ft/hour] to describe how fast she removes the snow, and you're asked for a function to describe how much snow [cubic feet] has been removed. so to achieve this, you need to integrate her rate function. since the rate function is piece-wise, your result will be too. from t=0 to t=6, no snow has been removed, so h(t)=0.
from t=6 to t=7, she is removing snow at a rate of 125 cubic feet/hour, so you need to multiply the amount of time at this rate (t-6) times the 125. the reason that it's (t-6) instead of just t, is because if you're talking about 6:30 am for example, then only 30 minutes have been spent shoveling, not 6.5 hours.
from t=7 to t=9, she's shoveling at a rate of 108 cubic feet/hour, so again you need to multiply this rate times the time (t-7) again because you're talking about hours since 7 am that she's shoveling at this rate. the 125 is added to this number because that's how much snow she shoveled from 6 to 7 am.
i hope this clarifies things for you. if not, please ask more questions!
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